Leak localisation with a measure source convection-diffusion model
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918497033912320 |
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| author | Dang, Thi Tam Valkonen, Tuomo |
| author_facet | Dang, Thi Tam Valkonen, Tuomo |
| contents | We study the inverse problem of locating gas leaks from line-of-sight concentration measurements using a convection-diffusion model with the source term a Radon measure. By imposing sparsity-promoting regularisation on this measure, we recover point sources - identifying both their locations and intensities - rather than diffuse approximations. We jointly estimate the underlying physical convection (wind) and diffusion parameters. Our main theoretical contribution is the stability analysis of the convection-diffusion equation with respect to its parameters: the measure, and the convection and diffusion fields. Numerically, we employ a semi-grid-free optimisation approach for reconstructing the source measure. Our experiments demonstrate accurate localisation, highlighting the potential of the method for practical gas emission detection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12095 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Leak localisation with a measure source convection-diffusion model Dang, Thi Tam Valkonen, Tuomo Analysis of PDEs Optimization and Control We study the inverse problem of locating gas leaks from line-of-sight concentration measurements using a convection-diffusion model with the source term a Radon measure. By imposing sparsity-promoting regularisation on this measure, we recover point sources - identifying both their locations and intensities - rather than diffuse approximations. We jointly estimate the underlying physical convection (wind) and diffusion parameters. Our main theoretical contribution is the stability analysis of the convection-diffusion equation with respect to its parameters: the measure, and the convection and diffusion fields. Numerically, we employ a semi-grid-free optimisation approach for reconstructing the source measure. Our experiments demonstrate accurate localisation, highlighting the potential of the method for practical gas emission detection. |
| title | Leak localisation with a measure source convection-diffusion model |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2605.12095 |